A candidate for governor of a certain state claims to be favored by at least half of the voters. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
A) There is sufficient evidence to support the claim ? = 0.5.
B) There is not sufficient evidence to reject the claim ? = 0.5.
C) There is sufficient evidence to reject the claim ? = 0.5.
D) There is not sufficient evidence to support the claim ? = 0.5.

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

On this case we want to test is [tex]p>0.5[/tex] sicne the claim is that he is to be favored by at least half of the voters. The claim for this case would be on the null hypothesis since the null hypothesis is the only one that can contain the symbol equal.

So the correct system of hypothesis for this case would be:

Null hypothesis: [tex]p\geq 0.5[/tex]

Alternative hypothesis: [tex] p< 0.5[/tex]

Or in other way like this:

Null hypothesis: [tex]p= 0.5[/tex]

Alternative hypothesis: [tex] p> 0.5[/tex]

If we reject the null hypothesis the correct option would be:

C) There is sufficient evidence to reject the claim [tex]p \geq 0.5[/tex].